Definitely get him to a doctor. The stopping-breathing-then-choking thing is definitely a probable sleep apnea sign and can be dangerous: He really is ceasing to breathe for those few moments. Sleep apnea like that can be related to other health issue such as heart issues too so get him checked out. A friend's husband had those symptons and now uses a CPAP machine (I think that's what it's called) every night -- it's a device that fits over his mouth and nose and has made a huge difference.
Meanwhile: Without apnea in the picture, both husband and another friend's husband were doing a lot of nighttime coughing. In both our cases, we not only did a lot of sheet- and bedspread-washing, we ended up encasing our mattresses in non-allergenic mattress covers. In both cases it worked -- the husbands stopped the coughing once the mattresses were encased. Consider using a mattress cover -- it has to completely encase the mattress and be zipped shut and should be "hypo-allergenic" -- and/or replacing the mattress. Even if you get a new mattress I would still get a cover and use it immediately. You can have a very clean room, sheets, etc. but the mattress traps allergens including, yes, flakes from our own skin etc. It's worth a try.
But that should not take the place of an advanced workup and sleep study as soon as possible! He may indeed be allergic to something, but he should never assume that allergies alone are the problem. If he has sleep apnea, he needs treatment for that.